I've seen big sector contracts (e.g. 10k-100k employees) with it built in for a fixed number of years. Presumably the negotiators talked through some indicators originally.
I've also seen several 'eh, on average it's about 2%" type giving leading to a 2% written into your comp.
I've also seen places give it but not in your contract; based on execs opinion I guess on what real cost-of-living was doing. I suppose that's plausibly as accurate as picking an index.
The two concepts are so intertwined they are often rolled together.
FWIW I've seen contracts with separate clauses (e.g. something like everyone gets 2%, if you live in this city or this city you also get a 5% col adjustment). The non-inflation aspect of c-o-l changes is usual housing related and regional, I think (or based on remoteness)